The average of 31 numbers is 59. The average of the first 11 numbers is 53.9 and that of the last 21 numbers is 62.1. If the 11th number is excluded, then what is the average of the remaining numbers?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 58.7.
Average of all 31 numbers = 59 → Total sum = ( 31 × 59 = 1829 )
Average of first 11 numbers = 53.9 → Sum = ( 11 × 53.9 = 592.9 )
Average of last 21 numbers = 62.1 → Sum = ( 21 × 62.1 = 1304.1 )
The sum of:
First 11 numbers = 592.9
First 10 + Last 21 numbers = 592.9 – (11th number) + 1304.1 = Total – 11th number
11th number = ( 592.9 + 1304.1 – 1829 = 68 )
New sum = ( 1829 – 68 = 1761 )
New count = ( 31 – 1 = 30 )
New average =